Subgroups — #11763689

Order 1088.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63247	C₂	1	2	yes	maximal
2	C₂×#63225	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₁₇	C₄	1	1	yes	characteristic
4	C₂²×Dic₁₇	C₄	1	1	yes	characteristic
5	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
6	#63247	—	2	2	no	—
7	#63247	C₄	1	4	yes	complemented
8	C₂×#3624	—	2	2	no	—
9	#63225	—	2	2	no	—
10	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₇	—	2	1	no	—
12	C₂×C₄×C₁₇	—	4	1	no	—
13	C₂×Dic₁₇	—	2	1	no	—
14	C₂×Dic₁₇	—	4	1	no	—
15	C₂×Dic₁₇	C₂×C₄	1	2	yes	—
16	C₂×Dic₁₇	D₄	1	1	yes	characteristic
17	C₂×Dic₁₇	D₄	1	2	yes	—
18	C₂×Dic₁₇	Q₈	1	1	yes	characteristic
19	#3624	—	2	4	no	—
20	C₂²×C₁₇	—	2	1	no	—
21	C₂²×C₁₇	—	2	1	no	—
22	C₂²×C₁₇	C₄²	1	1	yes	characteristic
23	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
25	C₄×C₁₇	—	4	1	no	—
26	Dic₁₇	—	4	1	no	—
27	Dic₁₇	C₂²⋊C₄	1	2	yes	—
28	Dic₁₇	C₄⋊C₄	1	2	yes	—
29	#343	—	17	1	no	maximal, Sylow
30	C₂×C₁₇	—	2	1	no	—
31	C₂×C₁₇	—	2	1	no	—
32	C₂×C₁₇	#95	1	1	yes	characteristic
33	C₂×C₁₇	#100	1	1	yes	characteristic
34	C₂×C₁₇	#101	1	1	yes	characteristic
35	C₂×M₁₆	—	17	2	no	—
36	C₂×C₄⋊C₄	—	17	1	no	—
37	C₁₇	#343	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₄	—	17	1	no	—
39	C₂²×C₄	—	17	1	no	—
40	C₂²×C₄	#595	1	1	yes	characteristic
41	M₁₆	—	17	4	no	—
42	M₁₆	—	34	2	no	—
43	C₂×C₈	—	34	2	no	—
44	C₄⋊C₄	—	34	2	no	—
45	C₂³	C₂×#595	1	1	yes	characteristic
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	17	2	no	—
49	C₂×C₄	—	17	1	no	—
50	C₂×C₄	—	17	1	no	—
51	C₂×C₄	—	17	2	no	—
52	C₂×C₄	—	34	1	no	—
53	C₂×C₄	—	68	1	no	—
54	C₈	—	34	4	no	—
55	C₂²	—	2	1	no	—
56	C₂²	—	2	1	no	—
57	C₂²	C₄×#595	1	1	yes	characteristic
58	C₂²	C₄⋊#595	1	1	yes	characteristic
59	C₂²	C₂²⋊#595	1	1	yes	characteristic
60	C₄	—	4	1	no	—
61	C₄	—	17	2	no	—
62	C₄	—	17	2	no	—
63	C₄	—	68	1	no	—
64	C₂	—	2	1	no	—
65	C₂	—	2	1	no	—
66	C₂	#10587545	1	1	yes	characteristic
67	C₂	(C₂×#595)⋊C₄	1	1	yes	characteristic
68	C₂	#10587553	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#595
commutator	C₂²×C₁₇	C₄²
Frattini	C₂³	C₂×#595
Fitting	C₂²×C₄×C₁₇	C₄
socle	C₂²×C₁₇	C₂²⋊C₄
prime radical	C₂³×C₁₇	C₂×C₄
cosocle	C₂²×Dic₁₇	C₂²
hypercenter	C₂²×C₄	#595
hypocenter	C₁₇	#343
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
7. #63247	C₄	semidirect
37. C₁₇	#343	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#63247	2
C₂×#63225	2
#343	17